# Gauss Daily Challenge Questions

Week of December 11-15

Monday: How many of the five numbers 101, 148, 200, 512, 621 cannot be expressed as the sum of two or more consecutive positive integers?

(A) 0     (B) 1     (C) 2     (D) 3         (E) 4

Tuesday: Same as Monday

Wednesday: Given 8 dimes (10 ¢ coins) and 3 quarters (25 ¢ coins), how many different amounts of money can be created using one or more of the 11 coins?

(A) 27     (B) 29     (C) 35     (D) 26     (E) 28

Thursday: Same as Wednesday

Friday:  In the six-digit number 1ABCDE, each letter represents a digit. Given that 1ABCDE × 3 = ABCDE1, the value of A + B + C + D + E is

(A) 29      (B) 26       (C) 22      (D) 30       (E) 28

Monday:The value of 333 + 33 + 3 is

(A) 396    (B) 399       (C) 669     (D) 369        (E) 963

Tuesday: Which of the following is a multiple of 7?

(A) 75     (B) 76      (C) 77      (D) 78          (E) 79

Wednesday: Which of these fractions is larger than 1/ 2 ?

(A) 2/ 5      (B) 3/ 7     (C) 4 /7     (D) 3/ 8    (E) 4

Thursday:  The measures of two angles of a triangle are 25◦ and 70◦ . The measure of the third angle is

(A) 85◦      (B) 105◦      (C) 65◦        (D) 95◦     (E) 75◦

Friday: A box of fruit contains 20 apples, 10 oranges, and no other fruit. When a fruit is randomly chosen from the box, what is the probability that the fruit is an orange?

(A) 1/ 10       (B) 1 /20        (C) 1/ 30       (D) 1/ 3        (E) 2

Week 2

Tuesday: A larger cube has volume 64 cm3 . A smaller cube has edges that are half the length of the edges of the larger cube. What is the volume of the smaller cube?

(A) 24 cm3        (B) 48 cm3     (C) 8 cm3        (D) 16 cm3        (E) 27 cm3

Wednesday: Alex pays \$2.25 to take the bus. Sam pays \$3.00 to take the bus. If they each take the bus 20 times, how much less would Alex pay than Sam in total?

(A) \$25      (B) \$10          (C) \$15         (D) \$45 (         E) \$60

Thursday:Carrie is travelling at a constant speed of 85 km/h. If Carrie is halfway through a 510 km trip, how much longer will the trip take?

(A) 5 hours        (B) 425 hours      (C) 12 hours      (D) 1.5 hours           (E) 3 hours

Friday: Points P, Q and R are on a number line. Q is halfway between P and R. If P is at −6 and Q is at −1, then R is at

(A) 4      (B) −11     (C) 3        (D) −7        (E) 5

Week 3

Monday: Ahmed chooses two diﬀerent items for a snack. His choices are an apple, an orange, a banana, and a granola bar. How many diﬀerent pairs of snacks could he choose?

(A) 3   (B) 4     (C) 5       (D) 6      (E) 7

Tuesday: Sophia did push-ups every day for 7 days. Each day after the ﬁrst day, she did 5 more push-ups than the day before. In total she did 175 push-ups. How many push-ups did Sophia do on the last day?

(A) 55    (B) 35     (C) 50    (D) 45      (E) 40

Wednesday: The mean (average) of a set of six numbers is 10. When the number 25 is removed from the set, the mean of the remaining numbers is (A) 6     (B) 7     (C) 8     (D) 9      (E) 10

Thursday:  The eight vertices of a cube are randomly labelled with the integers from 1 to 8 inclusive. Judith looks at the labels of the four vertices of one of the faces of the cube. She lists these four labels in increasing order. After doing this for all six faces, she gets the following six lists: (1,2,5,8),(3,4,6,7), (2,4,5,7),(1,3,6,8),(2,3,7,8), and (1,4,5,6). The label of the vertex of the cube that is farthest away from the vertex labelled 2 is

(A) 3     (B) 4  (C) 5     (D) 6      (E) 7

Friday: Angie has a jar that contains 2 red marbles, 2 blue marbles, and no other marbles. She randomly draws 2 marbles from the jar. If the marbles are the same colour, she discards one and puts the other back into the jar. If the marbles are diﬀerent colours, she discards the red marble and puts the blue marble back into the jar. She repeats this process a total of three times. What is the probability that the remaining marble is red?

(A) 1/ 2    (B) 1 /4      (C) 2 /3      (D) 1/ 3     (E) 0